A193030 Decimal expansion of the coefficient of x in the reduction of e^(x/2) by x^2->x+1.

6, 7, 5, 9, 7, 7, 2, 4, 5, 8, 7, 2, 0, 5, 1, 0, 7, 7, 6, 6, 2, 2, 5, 9, 6, 3, 7, 4, 1, 7, 5, 6, 3, 0, 7, 0, 4, 1, 7, 1, 2, 0, 8, 6, 0, 5, 3, 2, 6, 1, 6, 1, 7, 4, 0, 0, 2, 1, 3, 8, 5, 4, 2, 3, 1, 3, 6, 0, 2, 9, 1, 8, 9, 5, 2, 8, 7, 7, 5, 3, 2, 1, 1, 4, 2, 1, 8, 5, 4, 2, 6, 8, 5, 0, 3, 7, 6, 6, 0, 9

Offset

0,1

Comments

Reduction of a function f(x) by a substitution q(x)->s(x) is introduced at A193010.

Links

Table of n, a(n) for n=0..99.

Formula

From Amiram Eldar, Jan 18 2022: (Start)

Equals Sum_{k>=1} Fibonacci(k)/(k!*2^k).

Equals 2*exp(1/4)*sinh(sqrt(5)/4)/sqrt(5). (End)

Example

0.675977245872051077662259637417563070...

Mathematica

f[x_] := Exp[x/2]; r[n_] := Fibonacci[n];
c[n_] := SeriesCoefficient[Series[f[x], {x, 0, n}], n]
u1 = N[Sum[c[n]*r[n], {n, 0, 100}], 100]
RealDigits[u1, 10]

Crossrefs

Cf. A000045, A193010, A192232, A193029.

Sequence in context: A021152 A199720 A157122 * A035414 A020505 A171538

Adjacent sequences: A193027 A193028 A193029 * A193031 A193032 A193033

Keyword

nonn,cons

Author

Clark Kimberling, Jul 14 2011

Status

approved